fieldable/isFieldable() in the entity type annotation/on EntityTypeInteface is misnamed. It is not about having fields, the point is being able to add/update/remove fields, like field.module does.
Same for the FieldableEntityStorageInterface,
Remove the flag completely. All content entities are supposed to support it if the storage supports it. The only thing that has to be specified is the field_ui_base_route, that tells field_ui where the integration point is for the Manage fields and related local tasks. The interface is renamed to DynamicallyFieldableEntityStorageInterface and also rename the corresponding FieldableEntityStorageSchemaInterface to DynamicallyFieldableEntityStorageSchemaInterface.
There are now 3 different things to check for, depending on what the code is doing:
1. Can have fields/is a content entity:
// On the entity. there is an issue that adds a FieldableEntityInterface.
$entity instanceof ContentEntityInterface.
// On the entity type. This is not great DX, but there is an issue for this too.
Use case: Check if an entity type can have fields. Every content entity type has at least one base field, and config entity types do not have any fields.
2. Check if the storage allows for field (storages) to be added, removed, or updated.
$entity_manager->getStorage($entity_type_id) instanceof DynamicallyFieldableEntityStorageInterface
Use case: As a module storing data for other/all entity types, check which entity types that can be done for.
3. Check if field UI is enabled for a given entity type.
\Drupal::moduleHandler()->moduleExists('field_ui') && $entity_type->get('field_ui_base_route')
Use case: Extend/integrate with field UI.
Additionally, the onBundleCreate(), onBundleRename() and onBundleDelete() methods are moved from DynamicallyFieldableEntityStorageInterface to a new EntityBundleListenerInterface, similar to EntityTypeListenerInterface. The entity manager now also implements the same interface instead of slightly different methods. The order of arguments has been adapted and changed.
The UI for view modes, form modes and comment type creation is limited to entity types that specify a field UI base route. This is done because those all require the field UI to be used (manage displays, create comment fields).
User interface changes
As described above.
Original report by @fago
The entity definition / entity info key 'fieldable' does not fit any more - all content entities have fields now. So we should rename this + fix the name of FieldableEntityStorageControllerInterface // the base class to match that. We do not have that distinction yet anyway though, but I think this is where "field_ui" should move in the long-run.